A possible reason why feet might come together is for a lunge from standing position. Similarly when pressed in heavy sparring your feet may come together and you want to be able to take a big step to get some range. However, doing it with the feet together is really the basic way of showing and drilling the concept. Generally after that you might get yelled at for not being in a decent fighting stance.

Triangular footwork is good because you can step back and forward while evading attacks or to get flanking position. A close range example of this is circular footwork (eg. avoid a jab) and on the other side of the spectrum almost linear (to assist with attacking defending at long range). You can change the angle as much as you need to avoid or set something up, and of course theres the reverse triangle which is great for attacking while moving backward.